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Newly modified method and its application to the coupled Boussinesq equation in ocean engineering with its linear stability analysis

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Communications in Theoretical Physics 2020年第11期72卷 11-18页

作者： hajar farhan ismael Hasan Bulut Haci Mehmet Baskonus Wei Gao Department of Mathematics Faculty of ScienceUniversity of ZakhoZakhoIraq Department of Mathematics Faculty of ScienceFirat UniversityElazigTurkey Department of Mathematics and Science Education Harran UniversitySanliurfaTurkey School of Information Science and Technology Yunnan Normal UniversityKunmingChina

Investigating the dynamic characteristics of nonlinear models that appear in ocean science plays an important role in our *** this research,we study some features of the paired Boussinesq equation that appears for two-layered fluid flow in the shallow water *** extend the modified expansion function method(MEFM)to obtain abundant solutions,as well as to find new *** using this newly modified method one can obtain novel and more analytic solutions comparing to ***,numerical solutions via the Adomian decomposition scheme are discussed and favorable comparisons with analytical solutions have been done with an outstanding ***,the instability modulation of the governing equations are explored through the linear stability analysis *** new solutions satisfy the main coupled equation after they have been put into the governing equations.

关键词： newly modified method coupled Boussinesq equation linear stability analysis Adomian decomposition method

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Multi-Waves,Breathers,Periodic and Cross-Kink Solutions to the(2+1)-Dimensional Variable-Coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada Equation

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Journal of Ocean University of China 2021年第1期20卷 35-44页

作者： LIU Dong JU Xiaodong ILHAN Onur Alp MANAFIAN Jalil ismael hajar farhan State Key Laboratory of Petroleum Resources and Prospecting China University of PetroleumBeijing 102249China China Petroleum Materials Company Limited Beijing 100029China Department of Mathematics Erciyes UniversityMelikgazi-Kayseri 38039Turkey Department of Applied Mathematics Faculty of Mathematical SciencesUniversity of TabrizTabriz ***Iran Department of Mathematics Faculty of ScienceUniversity of ZakhoZakho 42002Iraq

The present article deals with multi-waves and breathers solution of the(2+1)-dimensional variable-coefficient CaudreyDodd-Gibbon-Kotera-Sawada equation under the Hirota bilinear operator *** obtained solutions for solving the current equation represent some localized waves including soliton,solitary wave solutions,periodic and cross-kink solutions in which have been investigated by the approach of the bilinear ***,by choosing specific parameter constraints in the multi-waves and breathers,all cases the periodic and cross-kink solutions can be captured from the 1-and *** obtained solutions are extended with numerical simulation to analyze graphically,which results in 1-and 2-soliton solutions and also periodic and cross-kink solutions *** will be extensively used to report many attractive physical phenomena in the fields of acoustics,heat transfer,fluid dynamics,classical mechanics,and so *** have shown that the assigned method is further general,efficient,straightforward,and powerful and can be exerted to establish exact solutions of diverse kinds of fractional equations originated in mathematical physics and *** have depicted the figures of the evaluated solutions in order to interpret the physical phenomena.

关键词： variable-coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada equation Hirota bilinear operator method soliton multi-waves and breathers periodic and cross-kink solitray wave solutions

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Multi-solutions with specific geometrical wave structures to a nonlinear evolution equation in the presence of the linear superposition principle

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Communications in Theoretical Physics 2023年第1期75卷 5-14页

作者： hajar F ismael Tukur Abdulkadir Sulaiman M S Osman Department of Mathematics Faculty of ScienceUniversity of ZakhoZakhoIraq Department of Computer Engineering Biruni UniversityIstanbulTurkey Department of Mathematics Faculty of ScienceCairo UniversityGiza 12613Egypt

Lump solutions are one of the most common solutions for nonlinear evolution *** study aspires to investigate the generalized Hietarintatype *** auspiciously provide multiple M-lump *** the other hand,collision phenomena to multiple M-lump waves with soliton wave solutions are also *** the collision,the amplitude of the lump will change significantly over the processes,whereas the amplitude of the soliton will just minimally *** it is of paramount importance,we use suitable values of parameter to put out the physical features of the reported results through three dimensional and contour *** results presented express physical features of lump and lump interaction phenomena of different kinds of nonlinear physical ***,this study serves to enrich nonlinear dynamics and provide insight into how nonlinear waves propagate.

关键词： the generalized Hietarintatype equation M-lump waves interaction phenomena hirota bilinear method

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Various exact wave solutions for KdV equation with time-variable coefficients

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Journal of Ocean Engineering and Science 2022年第5期7卷 409-418页

作者： hajar F.ismael Muhammad Amin S.Murad Hasan Bulut Department of Mathematics Faculty of ScienceUniversity of ZakhoZakhoIraq Department of Mathematics College of ScienceUniversity of DuhokDuhokIraq Department of Computer and communications Engineering College of EngineeringNawroz UniversityDuhokIraq Department of Mathematics Faculty of ScienceFirat UniversityElazigTurkey

In this study,we investigate the(2+1)-dimensional Korteweg-De Vries(KdV)equation with the extension of time-dependent coefficients.A symbolic computational method,the simplified Hirota’s method,and a long-wave method are utilized to create various exact solutions to the suggested *** symbolic computational method is applied to create the Lump solutions and periodic lump ***’s method and a long-wave method are implemented to explore single-,double-and triple-M-lump waves,and interaction physical phenomena such as an interaction of single-M-lump with one-,twosoliton solutions,as well as a collision of double-M-lump with single-soliton ***,the simplified Hirota’s method is employed to explore complex multi-soliton *** realize dynamics,the gained solutions are drawn via utilizing different arbitrary variable coefficients.

关键词： Hirota’s method Lump solutions Interaction phenomena Complex multi-soliton waves KdV equation

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Analyzing study for the 3D potential Yu-Toda-Sasa-Fukuyama equation in the two-layer liquid medium

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Journal of Ocean Engineering and Science 2024年第5期9卷 454-460页

作者： hajar F.ismael Ìsrafil Okumus Tolga Aktürk Hasan Bulut M.S.Osman Department of Mathematics Faculty of ScienceUniversity of ZakhoZakhoIraq Department of Mathematics Faculty of ScienceFirat UniversityElazigTurkey Department of Mathematics Faculty of ScienceErzincan Binali Yildirim UniversityErzincanTurkey Department of Mathematics and Science Education Faculty of EducationOrdu UniversityTurkey Department of Mathematics Faculty of Applied ScienceUmm Al-Qura UniversityMakkah 21955Saudi Arabia Department of Mathematics Faculty of ScienceCairo UniversityGiza 12613Egypt

In this work,we use the(m+1/G')-expansion method and the Adomian decomposition method to study the 3D potential Yu-Toda-Sasa-Fukuyama(3D-pYTSF)equation which has a good application in the twolayer liquid *** the first time,the(m+1/G')-expansion and the Adomian decomposition methods are used to establish novel exact wave solutions and to study some numerical solutions for the 3D-pYTSF equation,*** using the analytical method,kink-type wave,singular solution and some complex solutions to the suggested equation are successfully *** obtained wave solutions are represented with some figures in 3D and contour plots.

关键词： (m+1/G')-expansion method Complex solutions Adomian decomposition method

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